experimental analysis of wideband spectrum sensing

5390 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 68, NO. 9, SEPTEMBER 2020

Experimental Analysis of Wideband SpectrumSensing Networks Using Massive

MIMO TestbedI. Dey , Member, IEEE, P. Salvo Rossi , Senior Member, IEEE, M. Majid Butt, Senior Member, IEEE,

and Nicola Marchetti , Senior Member, IEEE

Abstract— In this paper, we investigate the practical impli-cation of employing virtual massive multiple-input-multipleoutput (MIMO) based distributed decision fusion (DF) for col-laborative wideband spectrum sensing (WSS) in a cognitive radio(CR)-like network. Towards that end, an indoor-only measure-ment campaign has been conducted to capture the propagationstatistics of a 4×64 massive MIMO system with one authorizedprimary user (PU) and 4 unauthorized secondary users (SUs)transmitting simultaneously over a 20 MHz band divided into1200 subcarriers. The frequency subcarriers belong to anOrthogonal-frequency-division-multiplexing (OFDM)-like set-upwithout the addition of cyclic prefix (CP) to the transmit symbols.Measurements are accumulated for different relative positions ofthe SUs which are analyzed to extract fading, shadowing, noiseand interference power statistics. Log-likelihood ratio (LLR)based fusion rule and three different sets of sub-optimum fusionrules along with their time-reversed versions are formulatedfor combining decisions on the availability of each subcarriertransmitted by the SUs. The extracted channel characteristicsare incorporated in both analytical and simulated performanceanalysis of the devised fusion rules for comparison and testing thevalidity of distributed DF in realistic collaborative WSS scenario.

Index Terms— Wideband spectrum sensing, massive MIMOchannel measurement, fading, shadowing and interference, fusionperformance.

I. INTRODUCTION

COGNITIVE Radio (CR) promises coherent and efficientsharing of available spectrum between authorized Pri-

mary Users (PU) and unauthorized Secondary Users (SUs).The SUs are accommodated on the same bandwidth as the PUonly when the PU is inactive. A major challenge in implement-ing CR networks in densely deployed areas is the design ofdynamic spectrum sensing and spectrum allocation algorithms

Manuscript received August 13, 2019; revised December 16, 2019 andApril 4, 2020; accepted May 18, 2020. Date of publication May 29, 2020;date of current version September 16, 2020. This work was supported byEDGE through the Marie Skodowska-Curie COFUND Actions under Grant13236/203377. The associate editor coordinating the review of this article andapproving it for publication was W. Chen. (Corresponding author: I. Dey.)

I. Dey is with CONNECT, National University of Ireland, Maynooth,W23 F2K8 Ireland (e-mail: [email protected]).

P. Salvo Rossi is with the Department of Electronic Systems, NorwegianUniversity of Science and Technology (NTNU), 7491 Trondheim, Norway(e-mail: [email protected]).

M. Majid Butt is with Nokia Bell Labs, 91620 Nozay, France (e-mail:[email protected]).

Nicola Marchetti is with CONNECT, Trinity College Dublin, Dublin 2,D02 YY72 Ireland (e-mail: [email protected]).

Color versions of one or more of the figures in this article are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TCOMM.2020.2998544

for SUs without disturbing the existing PU. Spectrum sens-ing detects unused bandwidth portions dynamically withoutinterfering with the activity pattern of the PU. CollaborativeWideband Spectrum Sensing (WSS) techniques accomplishthe task of scanning multiple bands jointly or sequentially byexploiting spatial diversity and thereby improving the decisionreliability on the availability of chunks of the spectrum [1], [2].

Distributed collaborative spectrum sensing performs betterthan the centralized option, especially in presence of fadingand shadowing [3], [4]. It is to be mentioned here thatcollaborative spectrum sensing refers to a distributed sensingphase and centralized spectrum sensing alludes to a non-distributed processing phase. For distributed spectrum sensing,individual SU senses each of the available frequency bandsand transmits its decision on the presence/absence of the PUon each of these bands to a Decision Fusion Center (DFC).The DFC implements array processing using different decisionfusion rules through multiple antennas (small, moderate andlarge array) and combines all the SU decisions to arrive at theright one [5], [6]. However, all collaborative DF rules to datehave only been proposed for narrowband spectrum sensing.As a consequence, their performance have only been evaluatedin presence of Additive White Gaussian Noise (AWGN) andnarrow-band fading over the propagation channel. Widebandchannel impairments like frequency-selective fading, interfer-ence between closely-spaced frequency bands and fast largescale channel effects have never been considered when testingthe effectiveness of the sensing and fusion algorithms.

Starting from the results in [6], in this paper, we considera measurement campaign with small number of SUs transmit-ting their decisions on spectrum availability over interferingreporting channels. The appeal of the above setup has beenrecently confirmed experimentally through real measurementcampaigns [7], [8]. We employ large number of receive anten-nas at the DFC, following the success observed in [9], [10] andthereby, mimicking a ’virtual massive MIMO communicationscenario’. This follows from the idea that the advantagesoffered by massive MIMO will be really useful in the contextof distributed decision making.

The decision transmitted from SUs on a group of closely-spaced frequency bands of interest (for e.g., OrthogonalFrequency Division Multiplexing (OFDM) based radio fre-quency (RF) communication system) will suffer from Inter-Symbol Interference (ISI), Inter-Carrier Interference (ICI) andInter-Link Interference (ILI) during the reporting phase [11].

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DEY et al.: EXPERIMENTAL ANALYSIS OF WSS NETWORKS USING MASSIVE MIMO TESTBED 5391

In such a scenario, the reliability of WSS can be improved byutilizing the correlation of cyclic prefix (CP) in multi-carriersignals. In order to take the advantage of both multi-carrier andmassive MIMO technologies, combining them is a promisingoption. In that case, addition of CP reduces the availabletime for data transmission resulting in degradation of spectralefficiency in multi-user networks [12]. The possibility of elim-inating (or shortening) CP lengths at the cost of additional ISI,ICI and ILI has been the focus of recent research in this area[13]. Though several interference cancellation techniques exist[14]–[16], the computation complexity increases exponentiallywhen employed in conjunction with massive number of receiveantennas.

If we want to apply the general framework of distributedDF to the OFDM-based collaborative WSS to address themajor challenges in wideband CR networks, we have to relyon the assumption that number of antennas at the DFC ismuch larger than the number of transmitting SUs. In thatcase, we have to eliminate the use of CP in order to maintainhigh spectral efficiency in dense network scenarios. Rather,we have to depend on the large array gain of massive MIMOto average out the ISI, ICI and ILI introduced by the closely-spaced frequency bands in an OFDM-based system withoutCP. Moreover, to analyze the performance of OFDM-basedWSS networks with collaborative DF, we have to characterizethe propagation environment and the interfering componentsas the fusion rule statistics in many cases are proportional tochannel coefficients (comprising of both large and small scalestatistics) and are dependent on the instantaneous channel stateinformation (CSI) [17], [18].

Despite the significance of the propagation statistics,no measurement campaigns have been performed specificallyfor evaluating WSS techniques for wideband CR networksover the years. The few that are conducted are generallymodeling spectral occupancy [19], [20] or they are applicationspecific [21] for spectrum detection and scanning techniques.To the best of our knowledge, there is no in-depth experi-mental investigation of the channel statistics (both small scaleand large scale statistics) of the propagation channel andinterference between competing SUs and DFC equipped withmassive number of antennas that then incorporate them forperformance evaluation of collaborative WSS techniques.

As massive MIMO systems are promised to be a part offuture generations of telecommunication networks, a largenumber of measurement campaigns have been conductedto characterize the propagation channel. In recent years,the major focus has been system metrics for multi-user sce-narios like spectral efficiency, capacity etc. [8], [22], [23], userseparation and channel orthogonality [24], [25], propagationmetrics over several frequency bands like pathloss, delayspread, coherence bandwidth [26] and root-mean-squared(rms) delay spread of the equivalent combined channel forlinear precoding schemes [27]. Propagation environment char-acterization has also been the focus of [28] and [29] targeting5G communication scenarios or [30], [31] for urban maro-cellular or micro-cellular environments. However, measure-ment campaign emulating wideband CR network-like scenariowith distributed detection applied over large antenna array atthe receiver has never been attempted before. Neither realistic

propagation measurements have been incorporated to evaluateperformance of fusion rules for collaborative WSS, especiallyin scenarios where the available frequency bands belong to amulti-carrier (OFDM-like) based RF communication system.

The primary contribution of this paper is two-fold. Firstly,we present a first-of-a-kind measurement campaign emulatinga cognitive radio like network where several users (secondary)collaborate to take decision on the availability of the spectrumunder the condition that the user (primary) licensed to use it isnot communicating at all. The aim is to characterize the propa-gation environment between multiple SUs (each SU equippedwith a single antenna) and DFC equipped with a large-sizeantenna array. The SUs jointly monitor multiple closely spacedfrequency bands belonging to an OFDM-like set-up in absenceof CP. In this study, we focus on ISI and ICI powers along withlarge and small scale channel statistics for each measurementroute, location and spatial distribution of the transmit nodes.The channel statistics obtained are directly incorporated inboth analytical and simulation based performance analysis of alarge range of sub-optimum DF rules. We derive sub-optimumDF techniques with reduced complexity for the received signalat the DFC consisting of (i) Widely Linear (WL) rules, (ii)Standard Maximal Ratio Combining (MRC) and (iii) modifiedMRC (mMRC), generalizing to our setup those introducedin [32] for massive MIMO DF context. Towards this end,large-MIMO and wideband version of each fusion techniqueis developed.

Secondly, a new set of time-reversal (TR) based sub-optimum fusion rules; (iv) Time-Reversal WL (TR-WL),(v) Time-Reversal MRC (TR-MRC), and (vi) modified TR-MRC (TR-mMRC), are applied and analyzed to mitigate theadditional interference incurred over closely spaced frequencybands due to removal of CP. For this set of DF rules,interference compensation is done through spatio-temporalfocusing. The (TR-) WL and (TR-) MRC set of rules areparticularly developed, as they are quite generic in natureand their performance do not necessarily vary a lot with theenvironments (indoor or outdoor). The MRC and mMRC donot require any assumption on the statistical distribution of thechannel and the SU decision process (since they are ideallyassumed to be error-free). On the other hand, WL set of rulesdepends on different reliabilities of the different SUs and takesinto account the accuracy of the sensing process. Thereforeperformance analysis of (TR-) WL and (TR-) MRC set ofrules will provide a clear picture of how distributed DF willperform in realistic collaborative WSS scenario.

The paper is organized as follows: Section II details themeasurement set-up, scenario and the process by whichinformation is extracted from the collected data. Section IIIprovides results from analyzing the collected measurements.Section IV formulates different DF rules and compare theirperformance in realistic environment using the channel statis-tics derived from the measurement, while Section V concludesthe paper.

1ILI is observed in outdoor scenarios, where the users are considerably faraway from the Fusion Center (FC). Since we conduct our measurements inindoor scenario with only 4 SUs communicating simultaneously, we neglectpresence of any ILI component.



Notations: Lower-case (resp. upper-case) bold letters denotevectors (resp. matrices), with ak (resp. an,m) representingthe kth element (resp. (n,m)th element) of a (resp. A);(·)t denotes transpose and E{·}, V{·}, R{·}, ∠(·), (·)†, and|| · || represents mean, variance, real-part, phase, conjugatetranspose and Frobenius norm operators, respectively; IN

denotes the N × N identity matrix; 0N (resp. 1N ) denotesthe null (resp. ones) vector of length N ; a (resp. A) denotesthe augmented vector (resp. matrix) of a (resp. A) i.e., a �[at a†]t (resp. A � [At A†]t); P (·) and p(·) are used todenote probability mass functions (PMF) and probability den-sity functions (PDF); N (μ,Σ) and NC(μ,Σ) denote normaldistribution and circular symmetric complex normal distrib-ution with mean vector μ and covariance matrix Σ respec-tively; Q(·) is used to denote the complementary cumulativedistribution function (CCDF) of standard normal distribution;χ2

k (resp. χ′2k (ξ)) denotes a chi-square (resp. a non-central

chi-square) distribution with k degrees of freedom (resp. andnon-centrality parameter ξ) and ‘mod L’ refers to the modulo-operation which returns the remainder after division by L.

II. MEASUREMENT CAMPAIGN

A. Measurement Scenario

The time-varying channel impulse response (CIR) of 4×64multiple-input-multiple-output (MIMO) channels with a centerfrequency of 2.45 GHz with 20 MHz bandwidth is recordedover this entire campaign. The room and the location ofthe transmitters are chosen such that they include both line-of-sight (LOS) and non-LOS (NLOS) communication paths,shadowing due to variety of electrical and laboratory equip-ments and pathloss due to building materials like dry-wall,glass, etc. The campaign is conducted in the circuits andantennas laboratory room located on the 5th floor of the Elektrobuilding at Norwegian University of Science and Technology(NTNU), Trondheim, Norway using the Re-configurable RadioNetwork Platform (ReRaNP). The room has dimensions of 9meter(m) in length, 7m in width and 3m in height.

The measurement scenario considered in this paper isrepresentative of a wide variety of environments. The SUsand the DFC are deployed within a single room, therebyreplicating a high user-density situation; a scenario that willbe encountered more frequently in near future with massiveInternet-of-Things (IoT) networks in smart homes and smartbuilding-like environments. The campaign is conducted in alaboratory room devoid of windows, but filled with differentmeasuring equipments. Therefore, the measurement scenarioalso covers smart industry-like environment with several noisyelectrical and automation equipments. The room is also a bitlarger than a standard office room, thereby representing anopen smart office-like environment, where several users, eitherstationary or with restricted movement, can access the networkat the same time.

The transmit antennas are omni-directional rubber duckdipoles and are deployed simultaneously at a height of 1.3m atdifferent locations of the room replicating an open laboratoryenvironment. The receive antennas are set up with the radioson a metallic framework and are also omni-directional. Eachmeasurement set is repeated for a stationary scenario and

Fig. 1. Example of experiment set-up for L7 scenario of the indoormeasurement campaign conducted in the circuits and antennas laboratory ofNTNU, Norway.

people moving around. In both cases, each measurement setis recorded for 107 snapshots, each snapshot being 5.5μslong. Therefore, each measurement set is recorded for anapproximate total of 55 secs. Due to channel reciprocityconditions, it is assumed that channel estimates can be usedfor both uplink and downlink.

The omni-directional transmit antennas are moved aroundthe laboratory room at 8 different set of measurement loca-tions. Among these locations, four sets (L1 - L4) have LOSconditions with two being obstructed LOS (L3, L4) dueto presence of glass wall between the transmitters and thereceivers. The rest of the four sets (L5 - L8) have NLOSpropagation with two (L5, L6) being cases where the transmit-ters and receivers are separated by one and two sets of dry-walls respectively. An example scenario representing NLOSpropagation condition i.e. L7 is shown in Fig. 1.

For propagation characterization, we consider a widebandcollaborative spectrum sensing network with transmitters emu-lating secondary users (SU) (K = 4) who are looking to trans-mit on a frequency band if the primary user (PU) authorized totransmit on that band is silent. Therefore, we are emulating anuplink communication scenario, where the sensing informationfrom the SUs on the different frequency bands are transmittedto a DFC equipped with multiple antennas (the number ofantennas at the DFC is way more than the number of SUs).



Fig. 2. System model for measured collaborative WSS network.

Let N denotes the total number of antennas at the DFC. Forour measurement set-up, each SU is equipped with only onetransmit antenna and N = 64. A system model is presentedin Fig. 2 to depict the communication scenario.

Out of 8 different measurement scenarios, for the firsttwo cases L1, L2 and the last two cases L7, L8, the fourSUs are located close to each other with only 2-3m inter-spacing where signal separation is difficult. While for theother set of scenarios, L3, L4, L5 and L6, the users arefar away from each other with more than 25 m of spacingand are separated by partitions like glass-wall and dry-walls.These set of scenarios represent condition, where good channelorthogonality is expected at the receiver station. Therefore,four different propagation conditions are investigated,

• Transmitting units close to each other at L1 and L2 havingLOS path to the receiver station (hereafter we will referto as ‘Tx-cls-LOS’)

• Transmitting units close to each other at L7 and L8 havingNLOS path to the receiver station (hereafter referred toas ‘Tx-cls-NLOS’)

• Transmitting units far apart from each other at L3 and L4having LOS path to the receiver station but separated byglass walls (hereafter we will indicate as ‘Tx-far-LOS’)

• Transmitting units far apart from each other at L5 and L6having NLOS path to the receiver station but separatedby set of dry-walls (further entitled as ‘Tx-far-NLOS’).

B. Measurement Set-Up

This subsection articulates the details of the ensemble ofequipments used to conduct an indoor large-scale MIMObased measurement campaign. In this campaign, 4 single-antenna stationary transmitters deployed within the transmis-sion power range of the base station (BS), are used to sendtheir decisions regarding a certain phenomenon to the BS,which in this case acts as a DFC. The transmit units (SUs)are prototyped using the Universal Software Radio Periph-eral (USRP) Re-configurable I/O (RIO) with an integratedGlobal Positioning System Disciplined Oscillator (GPSDO)and single-input-single-output (SISO) wireless capabilities.

Each USRP RIO represents two SU modules. The DFC isimplemented using USRP-RIO equipped with 64 synchronized

Fig. 3. Block diagram of measurement set-up.

omni-directional antenna ports forming a switched antennaarray with 32 dual-polarized patches arranged with 32 ele-ments in an equally spaced 4 × 8 rectangular configuration.The DFC consists of 2 units, each containing 32 radio chainsby employing 16 National Instruments (NI) USRP-2943Rdevices. The framework implements a TDD system withan OFDM-like physical layer with 20 MHz bandwidth ofoperation. The DFC antenna array consists of wideband LongPeriodic Dipole Arrays (LPDAs) with operating frequencyranging between 1.5 GHz and 6 GHz. The linearly polarizedLPDA elements have half-power bandwidth of approximately110◦ in the azimuth and 70◦ in the elevation giving a directivegain of 6dBi when used as a single element.

An overview of the measurement set-up is provided throughthe block diagram in Fig. 3. The 64 antenna MIMO testbedis controlled through a mounted PXI chassis and a PC centerused for recording and conducting experiments. The system isdesigned with the LabVIEW Communication System DesignSuite 2.0 running on USRP software defined radios (SDRs)allowing scaling from a 4-antenna upto an 128-antenna system.It is to be noted here that the antenna elements are placed110 mm apart each with interleaved polarization orthogonalto its neighboring element thereby minimizing correlationbetween consecutive antenna elements. A common groundplane is placed behind the array elements which results insome variations in the directivity gain of the antenna elements.

Settings of two main files are configured for running theexperiments: the mobile station (MS) host and the base stationhost. The base station host is meant to run on the unitcontrolling the 64-antenna set-up acting as DFC, where themobile station should run on all the units emulating the SUs.The MIMO application framework does have functionality tocalculate properties such as the impulse response, frequencyresponse and power spectrum for the various channels betweenthe BS and the MS, but said properties are only stored in atemporary data buffer for a few millisecond before they arediscarded. Therefore, in order to save the data to some storageformat, the BS and MS .gvi files are modified to continuouslysave various types of measurement samples to text files storedlocally on the host computers.

Note on Software Modification

In order to implement the spectrum sensing frameworkwithin the measurement campaign set-up, the software files inthe BS and MS configuration are modified to implement PUand SU functionalities. The host computer that controls theSUs, UE 3 and UE 4, is also programmed to control the SDR



Fig. 4. CIRs observed at the DFC from each SU for measurement scenario L5 with people moving around in the measured indoor area.

acting as the PU. The PU implementation is designed in sucha way that if the PU is silent, nothing is transmitted, whereasif active, a random bit sequence of 1s and 0s are created,then modulated with a BPSK modulation scheme at a carrierfrequency specified by a control on the program panel, andfinally broadcasted through the associated transmit antenna.

The carrier frequency is controlled using the program panel.It is varied between 2.44 and 2.46 GHz. However, the carrierfrequency is kept fixed for each set of measurement. TheSU implementation is designed to iteratively scan a certainspectrum region, each scan containing a center frequency anda certain bandwidth, where the entire spectrum is divided intoseveral sub-carriers for the spectrum sensing network modelpresented in Section IV. For each scan, the power spectrum iscomputed and the peak power spectrum value is compared toa threshold value of −50 dB.

A value above the threshold means PU activity, whereas a value below means that there is only noise present inthe spectrum and therefore means no PU activity. When theBoolean PU lth sub-band activity indicator is switched on,the SUs are supposed to transmit a BPSK modulated symbolof {+1} on the lth sub-band. When the PU is inactive, the SUswill transmit {−1} on the lth sub-band. An overall 20 MHzband with center frequency of 2.45GHz is scanned for eachmeasurement set and is divided into 1200 sub-carriers (i.e.L = 1200) with sub-carrier spacing of 15 KHz. Each of thesingle-antenna stationary SU transmits pilot symbols on all the1200 sub-carriers during the channel estimate acquisition.

The SUs transmit their single-slot BPSK modulated localdecisions {+1} or {−1} in parallel with the PU, only if theinterference level between PU and SU transmissions is lessthan the maximum amount of interference tolerable by the PU.Such a technique follows the popular underlay configurationfor CR networks [33] and assumes that the latency in thecollection of all the SU decisions at the DFC does not growwith the total number of SUs in the network. If the PU is silent,there is no interference between the PU and the SUs. If the PUis active on the lth sub-band, SUs transmit their local decisionsin parallel with the PU as long as the PU transmission achievesa target SINR of 30 dB.

C. Data Processing

The complex channel transfer function (CTF) coefficientH l

n,k over the lth sub-carrier between the kth SU and the nthantenna on the DFC is calculated by a minimum mean squared

error (MMSE) estimate of the received signal with the knownpilot symbols. The estimated CTF is denoted by H l

n,k. Thechannel impulse response (CIR) between the kth SU and thereceive set of antennas is obtained by taking inverse discreteFourier transform (IDFT) of the CTF to obtain,

hlk(z) = IDFT

l

{H l

n,k

}(1)

where z is the delay bin with Z = 107 denoting the totalnumber of delay bins or channel taps. Fig. 4 demonstratesan example set of CIRs for each SU observed at the DFCequipped with 64 receive antennas for dynamic measure-ment scenario at L5 over the sub-carrier band of 2449.97-2449.985 MHz (15KHz for each sub-carrier spacing).

The average received power from kth SU at location i iscalculated as

PR,k(i) =1N

∑n

∑z

|hlk(n, z)|2 (2)

and the average attenuation is given by,

Ak(i) = PR,k(i)/(αPT ) (3)

with PT as the transmit power and α as the additional lossesto account for. If logarithm of distance is plotted againstlogarithm of Ak(i), pathloss exponent (ν) can be determinedfrom the slope of the best fit line to the log-log plot. The PDFof deviation of each Ak(i) value from the best fit line to thelog-log plot yields the shadowing distribution.

To analyze the small scale fading statistics, the power delayprofile (PDP) of the channel is extracted by averaging thepower along the n-axis to yield a Z-element vector for eachSU. The average delay spread is the first moment of each SUinduced PDP on the lth sub-carrier and is given by,

τ l,k =∑

z τl,k(z)(

1N

∑n |hl

k(n, z)|2)∑z

(1N

∑n |hl

k(n, z)|2) (4)

The root-mean-squared (rms) delay spread is the square root ofthe second central moment of each PDP of each user channelon the lth sub-carrier given by,

βlk =

√τ2

l,k − (τ l,k)2 (5)

where

τ2l,k =

∑z τ

2l,k(z)

(1N

∑n |hl

k2(n, z)|2)∑

z

(1N

∑n |hl

k(n, z)|2)



Fig. 5. Shadowing distributions for all environments.

TABLE I

LARGE SCALE PARAMETERS

and the total PDP of each user channel on the lth sub-carrieris given by,

Blk =

(τl,k(1)

(1N

∑n

|hlk(n, 1)|2

), . . . ,

τl,k(Z)(

1N

∑n

|hlk(n,Z)|2

))t

(6)

The corresponding channel coherence bandwidth for each userantenna is calculated using 1/(5βl

k) [34].

III. MEASUREMENT RESULTS

A. Large Scale Channel Statistics

The shadowing distributions for LOS and NLOS scenariosare presented in Fig. 5. The pathloss exponents (ν) and meanand standard deviation (μλ, σλ) of the shadowing distribu-tions are averaged over the measured sub-carriers and aresummarized in Table I. Average values of μλ, σλ and ν aregrouped by the type of measurement location and scenario.Shadowing distributions for all the measurement scenarios canbe approximated using the Gamma distribution. The Pearson’schi-squared test [35] is used for verification of goodness of fitbetween Gamma and extracted shadowing distributions.

A very small variation in pathloss exponents is observedbetween different environments as the measurement campaignis executed in only one room and the distances between theSUs and the DFC are not varied much from one set of record-ings to the other. However, as the inter-SU distances and thedistances between the users and DFC increase, a large numberof different shadowing values are encountered resulting inhigher shadowing variance and increased shadowing severity.

Fig. 6. CDF of K-factor for all environments.

B. Small Scale Channel Statistics

The small scale fading statistics is extracted from theestimated frequency domain response, Hl

k ∈ CN×Z , whereH l

k(n, z) is the element on the nth row and zth column of Hlk.

The number of frequency response values with independentsmall scale fading between the kth SU and the DFC isRl

k = �ΩlSig/Ω

lCoh,k�, where Ωl

Coh,k is the discrete coherencebandwidth of the kth user channel over the lth sub-carrier andΩl

Sig is the total discrete bandwidth of the measurement signalof the lth sub-carrier. For the kth SU, the fading vector canbe defined by,

ξlk =

[|H lk(0, 0)|, . . . , |H l

k(N − 1, 0)|,|H l

k(0,ΩlCoh,k)|, . . . , |H l

k(N − 1, RlkΩl

Coh,k)|] (7)

Chi-squared goodness-of-fit test is applied to each of thefading vectors, ξl

k, for each SU against Rician distribution.A significance level of 5% [35] is used for verificationof goodness of fit. Rician K-factor is estimated for allmeasurements satisfying the Chi-square test using the methodof moments [36], the CDF plot of which is provided in Fig. 6.From the CDF plots of K-factors in Fig. 6, it is evidentthat lowest K-parameter is encountered if SUs are separatedby partitions (glass or dry-walls) and no LOS paths existbetween the SU and the DFC. Separation between the SUsleads to very low coordination between the users making thetransmit signals vulnerable to noise, interference and fading.

Assuming the kth transmit antenna being visualized as apoint-like source by the receive set of antennas, the steeringvector from the kth antenna U(φl

k) on the lth sub-carrier canbe formulated using,

u(φlk) = [1 ejπ cos(φl

k) ejπ2 cos(φlk) . . . ejπ(N−1) cos(φl

k)] (8)

where φk = 1N

∑n

∑z ∠hl

k(n, z). Therefore for each mea-surement set, there will be K such steering vectors for lth sub-carrier given by, U(Φl) = [u(φl

1),u(φl2), . . . ,u(φl

K)], sinceeach transmit antenna generates a separate steering vector overeach sub-carrier.



TABLE II

OBSERVED RANGE OF VALUES FOR K -FACTORS

Fig. 7. CDF of ISI power for all environments.

TABLE III

RANGE OF VALUES FOR INTERFERING POWERS

After extensive data fitting, it is possible to summarize andtabulate K-factors suitable for different indoor communicationscenarios in large-scale MIMO-based spectrum sensing net-work. The ranges of K-factors for Rician distributed channelsbetween the SUs and DFC are compiled in Table II.

C. Interference Analysis

The ReRaNP testbed operates on an OFDM like format,cyclic prefix (CP) has not been added to the sub-carriers.In that case, the channel between the SUs and the DFC willsuffer from inter-symbol interference (ISI) and inter-carrierinterference (ICI) which needs to be accounted for fusionperformance analysis in Section IV. Finally Table III providesthe range of values of ICI and ISI powers encountered for thefour different measurement scenarios.

1) Inter-Symbol Interference (ISI): We calculate the ISIpower within the lth sub-carrier after reception at the DFCusing the average delay spread τ l,k of (4), given by,

ψ2l,ISI =

K∑k=1

τ2l,k (9)

for large number of receive antennas at the DFC, i.e. N → ∞.The ISI power values for each sub-carrier are calculated foreach measurement location and the CDF of the values for bothLOS and NLOS scenarios are depicted in Fig. 7.

Fig. 8. CDF of ICI power for all environments.

TABLE IV

AVERAGE CHANNEL CAPACITY FOR DIFFERENT SCENARIOS

2) Inter-Carrier Interference (ICI): Similarly, we calculatethe ICI power from different neighboring sub-carriers on thelth sub-carrier after reception at the DFC using the mean-squared delay spread β

l

k of (5), given by,

ψ2l,ICI =

K∑k=1

L∑q=1

|βq

k(dql)|2 for q �= l (10)

for N → ∞ referring to a large array of receive antennas at theDFC. The ICI power values are calculated from the qth sub-carrier on the lth sub-carrier and dql is the distance betweenthe qth and lth sub-carriers (= 15 KHz between subsequentsub-carriers). The ICI power values for each sub-carrier arecalculated for each measurement location and the CDF ofthe values for both LOS and NLOS scenarios are depictedin Fig. 8.

In order to visualize how the interference varies withtransmit signal power and the location of the SUs in differentparts of the indoor environment, Fig. 9 illustrate interferingpowers as functions of transmit signal power. Interferencepower increases with the increase in transmit power and theinter-SU distances. As the end-to-end PDP decays, largernumber of multipath components arrive at the receiver. Thenumber of multipath components transferred to the DFC aremore in case of NLOS propagation scenarios than the LOSscenarios. Thus the interfering power increases faster withthe transmit signal power for the NLOS case than the LOSsituation.

D. Achievable Channel Capacity

The average uplink channel capacity achievable on eachsub-carrier (lth sub-carrier) can be calculated using,

Cl =1Z

Z∑z=1

log2 det

(IK +

ρl

KH l†H l

)(11)



Fig. 9. Total power of the interfering components at the DFC as a functionof the transmit signal power.

where ρl is the SINR on the lth sub-carrier. Average uplinkcapacity over the sub-carrier band of 2449.97-2449.985 MHzfor each measurement scenario is tabulated in Table IV forhigh (ρl = 2 dB) and low (ρl = 20 dB) interference occurringcases. Achievable uplink capacity exhibit mixed results. Bothin case of low and high SINR, higher capacity can be achievedwhen the SUs are far apart from each other. However, in caseof low SINR, LOS communication scenario exhibit highercapacity than the NLOS case contrary to the observation forthe high SINR cases.

IV. WIDEBAND COLLABORATIVE SPECTRUM SENSING

A. System Description

In this paper, we consider an OFDM-based cognitive-radiolike network with one PU and K unauthorized SUs findingopportunity to transmit in a licensed spectrum divided over Lfrequency sub-carriers, when the PU is inactive. Here, we willconcentrate on the SUs transmitting their decisions on eachsub-carrier, herein for the lth sub-carrier. Towards this end,we focus separately on sensing model of each SU and receivedsignal model concerning the reporting phase at DFC.

1) Sensing and Local Decision Model: The kth SU (k ∈K � {1, 2, . . . ,K}), equipped with a single antenna, sensesthe L frequency bands and transmits its local (1-bit) decisionon whether the PU is active or inactive in the lth sub-carrier.The local decision on lth frequency band is then mapped to aBinary Phase-Shift Keying (BPSK) modulated symbol, xl

k ∈X � {+1,−1} transmitted by the kth SU on the lth sub-carrier. Therefore, each SU transmits a total of L bits in eachtransmit symbol.

Let the hypothesis that the PU is active or silent on thelth frequency band be denoted by Hl

1 (resp. Hl0) and is

being transmitted on the lth sub-carrier. We assume that thelocal sensing and decision process at the kth SU over the lthsub-carrier is fully described by the conditional probabilitiesP (xl

k|Hli). Specifically, we denote the probability of detection

and false-alarm at kth SU on the lth sub-carrier as P lD,k �

P (xlk = 1|Hl

1) and P lF,k � P (xl

k = 1|Hl0), respectively.

Finally, for compactness, let xk �[x1

k · · · xLk

]t(resp. xl �[

xl1 · · · xl

K

]t) be the set of local decisions transmitted from

kth SU on the L sub-carriers (resp. from all the K SUs on lthsub-carrier).

2) Signal Model: The DFC is equipped with N receiveantennas over a wireless flat-fading multi-access channel; thisset-up determines a distributed or ‘virtual’ massive MIMOchannel. The N -length received vector at the DFC is denotedby yl �

(yl1, y

l2, . . . , y

lN

)twhere yl

n is the signal receivedby the nth receive antenna on the lth sub-carrier. A large-array configuration is considered here, that is N � K andthe communication process on the reporting channel for thelth sub-carrier may be viewed as a K × N massive MIMOsystem.

The discrete-time signal model (after matched filtering andsampling) for the received signal at the DFC is given by,

yl =√ρlGlxl + wl + Ψl (12)

where yl ∈ CN , Gl ∈ CN×K , xl ∈ χK , wl ∼NC(0N , σ

2w,lIN ) and Ψl ∼ NC(0N , ψ

2l IN ) are the received

signal vector, the channel matrix, the transmitted signal vector,the noise vector and the interfering signal vector respec-tively. In (12), the constant ρl denotes the energy spent byany of the SUs during the reporting phase. The componentfor interference Ψl in (12) arises from the combination ofISI among symbols carrying decisions of all K SUs on eachsub-carrier, and ICI due to nearby sub-carriers, and is givenby ψ2

l = ψ2l,ICI + ψ2

l,ISI.3) Channel Model: The channel coefficient vector gl

n,k canbe expressed as, gl

n,k =√λkhl

n,k for (n = 1, 2, . . .N, l =1, 2, . . .L), where λk accounts for pathloss and shadowingexperienced by the kth SU and remains constant over n and l.Each of the CIRs, hl

n,k can in turn be modeled as linear time-invariant finite impulse response (FIR) filters with the orderof Z , i.e., hl

n,k =(hl

n,k(0), . . . , hln,k(Z − 1)

)tand hl

n,k ∼NC(0, diag(Bl

k)) where the vector Blk =

(βl

k(0), . . . , βlk(Z −

1))t

is the PDP. Therefore, we have, Gl = Hl√

D (l =1, 2, . . . , L) where, Hl ∈ CN×K denotes the matrix of thefast-fading coefficients and D ∈ CK×K is a diagonal matrixwhere dk,k = λk.

The fading vector of the kth SU can be given by,

hRice,lk = κl

ku(φlk) +

√1 − κl

k2 hl

k (13)

filling the kth column of Hl. If ul(·) denotes the steering vec-tor with hl

k ∼ NC

(0N , IN

)characterizing the NLOS (scat-

tered) component, κlk

�=√

Klk

1+Klk

, where K lk is the Rician

K-factor between kth SU and DFC on the lth sub-carrier.4) Modified System Model: Here we develop the time-

reversed (TR) version of the channel model in order to formu-late the TR-based fusion rules. Let us denote the TR variant ofthe channel matrix on the lth sub-carrier as Gl. Each elementof Gl in this case can be expressed as, gl

n,k =√λkhl

n,k

for (n = 1, . . . , N, l = 1, . . . , L), where hln,k is the TR

version of hln,k, given by, hl

n,k = (hln,k(Z−1), . . . , hl

n,k(0))t.Essentially, hl

n,k becomes hln,k ∼ NC(0, diag(Bl

k)), where



Blk = [βl

k(Z − 1), βlk(Z − 2), . . . , βl

k(0)] is the TR versionof the channel PDP and

∑Z−1z=0 β

lk(z) = 1. Based on these

assumptions, we have Gl = Hl√

D where Hl denotes the TRchannel matrix containing the fading coefficients.

Since, we are assuming favorable propagation condition,the channel matrices Gl are pairwisely orthogonal. Hence theirtime-reversed versions are also pairwisely orthogonal to eachother and therefore, we can write, 1

N (Gl)†Gl ≈ Al. In thiscase, Al = D ∗ [diag(Bl

k)]. At the same time, the channelmatrix will also be pairwisely orthogonal to its time-reversedversion. Hence, as N → ∞, (Gl)†Gl ≈ 1

N Fl. In this case,

Fl =(√

D ∗[diag(

√Bl

k)])†

∗(√

D ∗[diag(

√Bl

k)])

.5) Performance Measures: We also assume that the SUs

are located in a circular area around the DFC with radiusrmax = 9 m uniformly distributed at random and we assumethat none of the SUs is closer to the DFC than rmin = 2 m. Thelarge-scale shadowing is characterized using λk = ζk( rmin

rk)ν ,

where ζk is a Gamma distributed random variable i.e. ζk ∼N (2μλ, σ

2λ/2), where μλ and σλ are the mean and standard

deviation in dB respectively. Also, rk is the distance betweenthe kth SU and the DFC and ν denotes the path-loss exponent(ν remains constant for all SUs over all the sub-carriers). Thenoise vector is generated according to wl ∼ NC(0N , σ

2w,lIN ),

where σ2w,l is the noise spectral density over the lth sub-

carrier. The interference vector is formulated according toΨl ∼ NC(0N , (ψ2

l,ICI + ψ2l,ISI)IN ). Consequently, we will use

the values of ISI (ψ2l,ISI) and ICI powers (ψ2

l,ICI) recordedin Table III depending on the propagation scenario.

Combining the decisions from all the K SUs independentlyon each sub-carrier, we can arrive at the total probabilities P l

D0

and P lF0

for the network for our chosen fusion algorithms.To compare the performance of different decision fusion rulesboth in terms of instantaneous sub-carrier (IS), system falsealarm and detection probabilities can be defined as,

P lF0

(γl,Gl) � Pr{Γl > γl|Gl,Hl

0

}P l

D0(γl,Gl) � Pr

{Γl > γl|Gl,Hl

1

}(14)

where γl denote the threshold with which the log-likelihoodratio (LLR) is compared to, and Γl is the generic statisticemployed at the DFC over the lth sub-carrier.

B. Fusion Rules

For comparison of fusion performance of the widebandspectrum sensing network, we consider four different deci-sion fusion rules, Log-likelihood Ratio (LLR) rule, WidelyLinear (WL) rules, Maximal Ratio Combining (MRC) andmodified MRC (mMRC) rules, proposed in [9], for singlefrequency carrier system. This set of rules aims at concludingon whether the PU is active or silent directly from the receivedsignal without processing the transmit signal.

1) Log-Likelihood Ratio (LLR) Rule: If the DFC is equippedwith large number of receive antennas i.e. N � K , the LLRtest statistics is given by,

ΓlLLR = ln

[�xl exp

(− ||yl−

√ρlGlxl||2

σ2e,l

)P(xl|Hl

1

)�

xl exp

(− ||yl−

√ρlGlxl||2

σ2e,l

)P(xl|Hl

0

)]

(15)

where ΓlLLR is the LLR for the LLR rule, σ2

e,l � σ2w,l + ψ2

l ,with σ2

w,l and ψ2l as the power densities of the noise and

interference processes respectively.2) Widely Linear (WL) Rules: If WL statistics is adopted,

ΓWLi,l � (al

WL,i)†yl and al

WL,i is chosen such that the deflectionmeasure is maximized following, al

WL,i � maxal:||al||2Di(al),where Di(al) � (E{ΓWL

l |Hl1} − E{ΓWL

l |Hl0})2/V{ΓWL

l |Hli},

D0(al) and D1(al) correspond to the normal and modifieddeflections respectively [4]. If WL statistics is adopted withdeflection measures D0(al) and D1(al), the correspondingfusion rules will be referred as ‘WL,0’ and ‘WL,1’ rulesrespectively. The expressions for al

WL,i can be given by,

alWL,i = Σ−1

yl|Gl,Hli

Glμμμli

/(∣∣∣∣∣∣Σ−1yl|Gl,Hl

i

Glμμμli

∣∣∣∣∣∣) (16)

following the proposition made in [9], where Σyl|Gl,Hli

=(ρlGlΣxl|Hl

i(Gl)† + σ2

e,lI2N

)and μμμl

i � 2[(P l

D,1 −P l

F,1

). . .(P l

D,K − P lF,K

)]t. In order to derive the exact IS

system probabilities for this fusion rule, we can define Γl,WBi,WL �

Γl,WLi

σe,land Γl,WB

i,WL|Gl,Hlj is distributed as Γl,WB

i,WL|Gl,Hlj ∼∑

xl∈χK P(xl|Hl

j

)N (E{Γl,WBi,WL|Gl,xl

}, 1)

where, for a largesystem,

limN→∞

(E{Γl,WB

i,WL|Gl,xl})

=N√

2ρl(μμμli)

txlVliD

lg

σe,l

√(μμμl

i)tVliDl

g(Vli)tμμμl

i

(17)

where

Vli � IK

−(1+σ2

w,l+∑K

k=1 τ2l,k+

∑Kk=1

∑Lp=1

∣∣βp

k(dpl)∣∣2

2Dlgρ

lN√NΣ−1

xl|Hli

)−1

(18)

for l �= p and Dlg = D ∗ [diag(Bl

k)].3) Maximal Ratio Combining (MRC) Rules: The LLR

in (15) can be simplified under the MRC fusion rule, i.e.P (xl = 1K |Hl

1) = P (xl = −1K |Hl0) = 1. In this case,

xl ∈ {1K ,−1K} and (15) reduces to,

ln

[exp

(− ||yl−

√ρlGl1K ||2σ2

e,l

)exp

(− ||yl+

√ρlGl1K ||2σ2

e,l

)]∝ R

{(al

MRC

)†yl}

� ΓlMRC

(19)

where, alMRC � Gl1K . In this case, we can define, Γl,WB

MRC �√2Γl

MRC

σe,l ||alMRC||

and evaluate the performance in terms of Γl,WBMRC .

In that case,

E{Γl,WB

MRC |Gl,xl}

=

√2ρl R{(1K)t(Gl)†Glxl}σe,l

√(1K)t(Gl)†Gl1K

(20)

where for a large system, i.e. as N → ∞,

limN→∞

(E{Γl,WB

MRC |Gl,xl})

=

√2 Nρl R{(1K)tDl

gxl}

σe,l

√(1K)tDl

g1K

(21)

Additionally, in order to exploit the linear SINR increasewith N , we can resort to an alternative form of MRC,



Fig. 10. Comparative ROC for the LLR fusion rule for different measuredlarge scale parameters (varying ν, μλ and σλ) with K = 4, N = 64 andRayleigh distributed fading vector.

denoted as modified MRC (mMRC) given by, ΓlmMRC �

R{(

almMRC

)†yl}

where, almMRC � Gl(Dl

g)−11K . We define,

Γl,WBmMRC �

√2Γl

mMRC

σe,l ||almMRC||

and evaluate the performance in terms

of Γl,WBmMRC as,

limN→∞

(E{Γl,WB

mMRC|Gl,xl})

=

√2 Nρl R{(1K)txl}

σe,l

√(1K)t(Dl

g)−11K

(22)

for a large system.

C. Time-Reversal (TR) Based Fusion Rules

Achievable SINR saturates at a certain deterministic levelin absence of CP if conventional DF rules like MRC, ZeroForcing (ZF), etc. are used at the DFC equipped with a massiveantenna array. This happens due to the correlation betweenthe combiner taps and the additional interference componentswhich do not average out with the increase in the number ofreceive and/or transmit antennas. In this section, we proposeapplication of time-reversal (TR) methods to alleviate this sat-uration problem. In order to exploit advantages of TR methodswhen applied to large array regime, we propose application ofTR-WL and TR-MRC fusion rules in collaborative WSS.

1) TR-WL Rule: The first approach consists of adoptingthe TR variant of the WL statistics such that, ΓTR-WL

i,l �(al

TR-WL,i)†yl where al

TR-WL,i can be explicitly expressed as,

alTR-WL,i = Σ−1

yl|Gl,Hli

Glμμμl

i

/(∣∣∣∣∣∣Σ−1

yl|Gl,Hli

Glμμμl

i

∣∣∣∣∣∣) (23)

following the formulation and proposition made in

Subsection IV-A, where Σyl|Gl,Hli

=(ρlG

lΣxl|Hl

i(G

l)† +

σ2e,lI2N

). Using the definition, Γl,WB

i,TR-WL � Γl,TR-WLi

σe,land the

test statistics Γl,TR-WLi being distributed as Γl,TR-WL

i |Gl,xl ∼N (E{Γl,TR-WL

i |Gl,xl},V{Γl,TR-WLi |Gl,xl}), Γl,WB

i,TR-WL|Gl,Hlj

will be distributed as Γl,WBi,TR-WL|Gl,Hl

j ∼∑xl∈χK P

(xl|Hl

j

)N (E{Γl,WBi,TR-WL|Gl,xl

}, 1). Here,

E{Γl,WB

i,TR-WL|Gl,xl}

=

√2ρl(μμμl

i)t(Gl)†Σ−1

yl|Gl,Hli

Glxl

σe,l||Σ−1

yl|Gl,Hli

Glxl||

(24)

As N → ∞, we have,

limN→∞

(E{Γl,WB

i,WL|Gl,xl})

=N√

2ρl(μμμli)

txlVliF

l

σe,l

√(μμμl

i)tVliAl(Vl

i)tμμμli

(25)

where

Vli � IK

−(1+σ2

w,l+∑K

k=1 τ2l,k +

∑Kk=1

∑Lp=1

∣∣βp

k(dpl)∣∣2

2AlρlN√NΣ−1

xl|Hli

)−1

for l �= p.2) TR-MRC Rules: The TR-MRC rule can be defined as,

alTR-MRC � Gl1K , and the test statistics as, Γl,WB

TR-MRC �√2Γl

TR-MRC

σe,l ||alTR-MRC||

and,

E{Γl,WB

i,TR-MRC|Gl,xl}

=

√2 Nρl R{(1K)tFlxl}σe,l

√(1K)tAl1K

(26)

for N → ∞. In order to exploit the linear SINR increase withN , we devise an alternative form of mMRC, denoted as time-reversed modified MRC (TR-mMRC) given by, Γl

TR-mMRC �R{(

alTR-mMRC

)†yl}

where, alTR-mMRC � Gl(Al)−11K . Thus

we can define, Γl,WBTR-mMRC �

√2Γl

TR-mMRC

σe,l ||alTR-mMRC||

and, in case of

N ∈ ∞, evaluate the performance in terms of Γl,WBTR-mMRC as,

E{Γl,WB

i,TR-mMRC|Gl,xl}

=

√2 Nρl R{(1K)t(Gl)†((Al)−1)†Glxl}

σe,l

√(1K)t((Al)−1)†1K

(27)

D. Performance Analysis

Assuming E{xl|Hl0} � (2 P l

F − 1)1K and E{(xl −E{xl|Hl

0})(xl − E{xl|Hl0})t|Hl

0} � [1 − (2 P lF − 1)2]IK ,

we can compute P lF0

for both WL and MRC set of rulesas below. It is to be noted here that, we can also computeP l

D0by assuming, E{xl|Hl

1} � (2 P lD − 1)1K and E{(xl −

E{xl|Hl1})(xl − E{xl|Hl

1})t|Hl1} � [1 − (2 P l

D − 1)2]IK .We first start with the argument that since P (yl|Gl,Hl

i)is assumed to follow Gaussian mixture distribution,Γl,WB

i,rule|Gl,Hli is also distributed according to Gaussian

mixture model that is,

Γl,WBi,rule |Gl,Hl

i

∼∑

xl∈χK

P (xl|Hli)

×N (E{Γl,WBi,rule|Gl,xl

},V{Γl,WB

i,rule |Gl,xl})

(28)



Using Gaussian moment matching [37], we can approximatethe pdf in (28) as,

Γl,WBi,rule |Gl,Hl

i

approx∼ N (E{Γl,WBi,rule|Gl,Hl

i

},V{Γl,WB

i,rule|Gl,Hli

}).

(29)

Since at low-SINR, the components of the Gaussian mixturegets concentrated within a certain region, we need to evaluatethe mean and variance of Γl,WB

i,rule |Gl,Hli separately for the

WL and MRC rules. For this purpose, let us define, Gl �=[

Glt Gl†]t and alm

�= 1

2

[al

mt

alm†]t

, where alm is either al

MRC,al

mMRC or alTR-mMRC depending on the fusion rules chosen from

the set of MRC and TR-MRC rules.Here we evaluate the mean and variance of Γl,WB

i,WL|Gl,Hli

as,

E{Γl,WB

i,WL|Gl,xl}

=

√ρl(μl

i)t(Gl)†Σ−1

yl|Gl,Hli

Gl E{xl|Hli}

||Σ−1yl|Gl,Hl

i

Glxl||(30)

and

V{Γl,WB

i,WL|Gl,xl}

=∑

xl∈χK

GlE{(xl − E{xl|Hl

i})

×(xl − E{xl|Hli})T |Hl

i}(Gl)† + 2σ2e,l (31)

Under simplifying assumptions of E{xl|Hl0} = (2 P l

F −1)1K

(31) becomes,

V{Γl,WB

i,WL|Gl,xl}

= [1 − (2 P lF − 1)2]Gl(Gl)† + 2σ2

e,l

≈ limK→∞

2(1 − δl2)K + 2σ2e,l (32)

where δl = (2 P lF − 1). Using (30) and (32) and exploit-

ing (29), we obtain the low-SINR approximation for P lF0

as,

P l,WLF0

≈ limN→∞

Q

(γl − Nδl√

2ρl(μli)

txlVliD

lg

σe,l

√(μl

i)tVl

iDlg(Vl

i)tμl

i√2(1 − δl2)K + 2σ2

e,l

)(33)

Next, we find the mean and variance of Γl,WBi,m |Gl,Hl

i as,

E{Γl,WB

i,m |Gl,xl}

=√ρlR{(al

m)†GlE{xl|Hl

i}}

(34)

and

V{Γl,WB

i,m |Gl,xl}

=∑

xl∈χK

(alm)†Gl

E{(xl − E{xl|Hli})

×(xl − E{xl|Hli})T |Hl

i}(Gl)†alm +

σ2e,l

2||al

m||2 (35)

where m represents MRC, mMRC, TR-MRC or TR-mMRCrules. Under simplifying assumptions of E{xl|Hl

0} = (2 P lF −

1)1K (35) becomes,

V{Γl,WB

i,m |Gl,xl}≈ lim

K→∞

√1/2((1−δl2)K+σ2

e,l) ||alm||

(36)

Fig. 11. Comparative ROC for the WL fusion rule for different measuredlarge scale parameters (varying ν, μλ and σλ) with K = 4, N = 64 andRayleigh distributed fading vector.

where δl = (2 P lF − 1). Using (34) and (36) and exploit-

ing (29), we obtain the low-SINR approximation for P lF0

as,

P l,mF0

≈ limN→∞Q

(γl−

√Nρlδl||al

m||2�1/2((1−δl2)K+σ2

e,l) ||alm||

). (37)

E. Performance Comparison

The fusion performance of a large scale MIMO-based WSNis investigated in this subsection over realistically distributedMIMO mobile radio channels. We will use Rician distributionto generate the channel fading vectors according to (13) forall scenarios with different ranges of K-factors for emulatingeach scenario.

1) Receiver Operating Characteristics (ROC): This sectionpresents the Receiver Operating Characteristics (ROC) (i.e.,PD0 v/s PF0 ) plots for the four fusion rules (one optimal andthree sub-optimal) propounded in Subsection IV-B with K = 4and N = 64 with an average channel SINR of 25 dB. Thechosen SINR is the direct consequence of the average valuesof the measured noise and interference power, transmit signalpower and the average attenuation calculated.

For the curves in Fig. 10, Fig. 11 and Fig. 12, we considerthe fading vectors hl

n,k ∼ NC(0, 1) to be Rayleigh distrib-uted. For the ‘No shadowing’ case in Fig. 11, we resort to(η, μλ, σλ) = (1, 0 dB, 0 dB). For all other results, in Fig. 10,Fig. 11 and Fig. 12, we use data from Table-I. Accordingto Fig. 10, presence of LOS components does not have anypositive impact on the LLR rule, while closeness of the SUsdo. The reason can be the fact that here we concentrate on thelarge scale channel parameters while small scale parametersare kept constant. In contrast, suboptimal rules like WL,MRC and mMRC do derive advantage of the presence ofthe LOS components and smaller inter-SU distances (Fig. 11and Fig. 12). The performance improvement depends on theability of the fusion rules to make more use of the systemknowledge (probability of correct detection, miss-detection



Fig. 12. Comparative ROC for the MRC and mMRC fusion rules for differentmeasured large scale parameters (varying ν, μλ and σλ) with K = 4, N =64 and Rayleigh distributed fading vector.

Fig. 13. Comparative ROC for all the fusion rules along with their TRversions for the Tx-cls-LOS scenario with K = 4, N = 64 accounting forboth large and small scale channel effects.

or false-alarm) and environment (shadowing, fading, noise,interference) statistics.

In order to ameliorate performance degradation resultingfrom the availability of reduced system knowledge andintroduction of interference due to channel impairments,we have introduced TR-based fusion rules in Section IV-C.In Fig. 13, we compare fusion performance of differentformulated fusion rules with their TR-versions over4 × 64 MIMO channel with Rician distributed vectorand large scale parameters equivalent to Tx-cls-LOSscenario i.e. (η, μλ, σλ) = (2.51,−1.43 dB,−4.9 dB). Thechannel parameters κl

k, ψ2l,ISI and ψ2

l,ICI are randomlygenerated in the ranges [κl

k,min, κlk,max] = [8, 9],

[ψ2l,ISI, min, ψ

2l,ISI, max] = [−55 dB,−35 dB] and

[ψ2l,ICI, min, ψ

2l,ICI, max] = [−60 dB,−50 dB] respectively.

Fig. 14. Comparative ROC for all the fusion rules along with their TRversions for the Tx-cls-NLOS scenario with K = 4, N = 64 accounting forboth large and small scale channel effects.

Fig. 15. Comparative ROC for all the fusion rules along with their TRversions for the Tx-far-LOS scenario with K = 4, N = 64 accounting forboth large and small scale channel effects.

For Fig. 14, we use [κlk,min, κ

lk,max] = [1.1, 5],

[ψ2l,ISI, min, ψ

2l,ISI, max] = [−55 dB,−35 dB] and

[ψ2l,ICI, min, ψ

2l,ICI, max] = [−74 dB,−36 dB] and large scale

parameters (η, μλ, σλ) = (2.37, 3.01 dB, 0.57 dB). equivalentto Tx-cls-NLOS. For Fig. 15, we choose [κl

k,min, κlk,max] =

[3, 11], [ψ2l,ISI, min, ψ

2l,ISI, max] = [−55 dB,−35 dB]

and [ψ2l,ICI, min, ψ

2l,ICI, max] = [−66 dB,−44 dB] and

(η, μλ, σλ) = (2.93, 3.42 dB, 3.54 dB) corresponding toTx-far-LOS and for Fig. 16, we resort to [κl

k,min, κlk,max] =

[0.75, 4], [ψ2l,ISI, min, ψ

2l,ISI, max] = [−54 dB,−36 dB]

and [ψ2l,ICI, min, ψ

2l,ICI, max] = [−65 dB,−45 dB] and

(η, μλ, σλ) = (3.12, 5.83 dB, 5.05 dB) according to thevalues obtained for Tx-far-NLOS.

From Fig. 13 - Fig. 16, it can be summarized thatWL,1 yields the best results after the LLR rule with MRC



Fig. 16. Comparative ROC for all the fusion rules along with their TRversions for the Tx-far-NLOS scenario with K = 4, N = 64 accounting forboth large and small scale channel effects.

yielding the worst performance. The mMRC rule alwaysperforms better than WL,0 and MRC as mMRC utilizes moresystem information than MRC, like fading and shadowingstatistics, PDP etc. This is in contrary to the observationsin [9] where the performance is simulated over a syntheticenvironment. On the other hand, WL,1 performs better thanWL,0 owing to its ability to exploit properties of more statisti-cal events observed; WL,0 employs characterization of Σxl|Hl

0while WL,1 utilizes knowledge on Σxl|Hl

1. This is in accor-

dance with the observations made in [9]. For large N , bothTR-MRC and TR-mMRC outperform MRC and mMRC. It isalso apparent that even when the SUs are far from each other,TR variants of WL and MRC become more appealing solu-tions than ordinary MRC or WL. However, TR-WL,1 offersbetter performance than TR-mMRC and TR-WL,0 performsbetter than TR-MRC. If no direct LOS communication pathexists between the SUs and the DFC, TR-MRC and TR-mMRC offers negligible performance improvement over theirnon-TR versions. The advantage offered by TR-mMRC overTR-WL,0 can be attributed to the fact that mMRC exploitsSINR increase for large N . The mMRC rule utilizes thechannel PDP to compute the test statistics, while WL,0 onlyuses the characterization of Σxl|Hl

0. When a large range of

interfering power values are encountered, TR-mMRC performsbetter than TR-WL,0, as mMRC takes advantage of moresystem knowledge like fading statistics and PDP vectors.

Fig. 16 demonstrates that TR-based rules offer very limitedimprovement in performance over the non-TR ones for thecase where the SUs are far apart without any LOS pathexisting between the SUs and the DFC. The reason can be thefact that TR-based methods take advantage of the degrees offreedom offered by the propagation environment; the larger thenumber of multipaths, the better is the fight against additionalinterference experienced. However, the present measurementcampaign, as conducted in an indoor-only environment, canonly experience a limited number of multipaths arriving atthe DFC. Such a small number of multipath components may

Fig. 17. Comparative analytical (‘anl’) and simulation (‘sim’) performancefor mMRC, TR-mMRC, WL,0 and TR-WL,0 rules in the Tx-cls-NLOSscenario with K = 4, N = 64.

Fig. 18. Comparative analytical (‘anl’) and simulation (‘sim’) performancefor MRC, TR-MRC, WL,1 and TR-WL,1 rules in the Tx-far-LOS scenariowith K = 4, N = 64.

not be enough to derive additional information regarding thepropagation environment.

It is noteworthy that, channel measurements collected inany other environment can be directly incorporated into thesystem modelling equations and fusion rule formulations,presented in this paper, to obtain performance analysis inthat particular environment. With the aim of generalization,we have derived equations to evaluate performance of theformulated fusion rules numerically in Section IV-D. We alsoestablish the validity of our derived expressions by comparingsimulated and analytical performance of different fusion rulesin Fig. 17 and Fig. 18. The analytical performances matchclosely, and many cases, almost identical to the simulatedperformances. The reason can be attributed to the fact that thechannel samples for the analytical results are generated usingthe same Ricean channel model (refer to (13)), as is used forgenerating the simulation results. This is done to replicate the



Fig. 19. PD0 v/s SINR for the case when the SUs are separated by partitions(glass or dry-wall) in a LOS scenario.

Fig. 20. PD0 v/s SINR for the case when the SUs are separated by partitions(glass or dry-wall) in a NLOS scenario.

practical propagation scenario as precisely as possible usingthe accumulated measurement data.

2) PD0 v/s SINR (dB): In Fig. 19 and Fig. 20, we plot thePD0 for the fusion rules, that come out to be the winners indifferent kinds of scenarios (LLR, WL,1, TR-WL,1, mMRCand TR-mMRC), as a function of the received SINR withPF0 ≤ 0.01 for different measurement scenarios. For the Tx-cls-LOS scenario, we use the same set of values for large andsmall scale channel parameters, as used for Fig. 13. Similarly,for the TX-cls-NLOS, Tx-far-LOS and Tx-far-NLOS, we reusethe channel parameters from Fig. 14, Fig. 15 and Fig. 16respectively. The LLR fusion rule exhibits saturation in thehigh SINR regime (from 20dB) for NLOS scenario when theSUs are placed far from each other (Fig. 20). Though the LLRrule utilizes more system knowledge (like large and small scalechannel statistics, noise and interfering power variance, depen-dence of output on detection hypothesis etc.) than any otherfusion rules, estimate of such system parameters is corruptedwith noise, ISI and ICI. Therefore, it is unable to combatresidual interference after a certain limit. While on the otherhand, the TR-based rules can leverage the channel reciprocityinformation continuously to improve their performance.

Fig. 21. PD0 v/s N for the case when the SUs are placed close to eachother in a LOS scenario.

Fig. 22. PD0 v/s N for the case when the SUs are separated by partitions(glass or dry-wall) in a NLOS scenario.

3) PD0 v/s N : In Fig. 21 and Fig. 22, we exhibit probabili-ties of detection PD0 with two groups of fusion rules (TR andnon-TR) as an interpolation function of the number of receiveantennasN under PF0 ≤ 0.01. For both the figures the channelSINR is fixed at 20 dB. The saturation effect that is observedin case of MIMO DF in Wireless Sensor Networks (WSN) [5]is not observed in case of the WSS scenario.

When the SUs are close to each other with a LOS pathexisting between the SUs and the DFC (refer to Fig. 21), forthe case of MRC, TR-MRC, WL,0 and TR-WL,0 rules, PD0

increases proportionally with the increase in N . The mMRC,TR-mMRC, WL,1 and TR-WL,1 rules exploit diversity gainbut do not reach saturation for the values of N and the channelSINR considered. However, the increase in PD0 is slower asN increases from 15 to 64 than as N increases from 1 to 15.

When the SUs are far from each other without any LOS pathexisting between the SUs and the DFC (refer to Fig. 22), forthe case of MRC and TR-MRC, as well as WL,1, mMRCand TR-WL,0 rules, PD0 increases proportionally with theincrease in N . The TR-WL,1 rule does not reach saturation for



the values of N and the channel SINR considered. However,the increase in PD0 is slower as N increases from 15 to64 than as N increases from 1 to 15. The increase in PD0

for the WL,0 rule is slowest as N increases from 1 to 15; rateof increase in PD0 increases from 15 to 35 and even morefrom 35 to 64. The increase in PD0 for the TR-mMRC ruleis slowest as N increases from 1 to 7; rate of increase in PD0

increases from 7 to 25 and even more from 25 to 64.

V. CONCLUSION

The main goal of this paper is to investigate and study thepractical implications of employing distributed detection forcollaborative WSS in a CR-like network, especially in thelight of the recently proposed decision fusion algorithms forDFC equipped with massive number of integrated antennas.The measurement set-up represents a scenario where the SUscompete for frequency bands closely-spaced as in case ofmulti-carrier systems like OFDM (though in absence of anyCP). This is accomplished through a measurement campaigncomprising of a 4 × 64 MIMO set-up using NI USRPs alldeployed in an indoor environments. The indoor environmentscan be static or dynamic (people moving around). Largeand small scale channel statistics as well as ISI and ICIcorrupting the transmit signal are captured for each measure-ment scenario and average values of pathloss and shadowingvariations are calculated for all cases. Shadowing statistics areobserved to follow Gamma distribution and fading statisticsare found to be well approximated by Rician distribution withvarying K-factors. The channel parameters and interferencepower encountered in the measured scenarios are directlyincorporated in the performance analysis of newly formulatedoptimal and sub-optimal fusion rules. Results demonstratethat closeness of the SUs benefits performance of all fusionrules. Presence of LOS propagation path also amelioratesperformance of sub-optimum rules. The results also demon-strate that mMRC performs better than WL fusion rule inrealistic scenario if WL statistics is employed with normaldeflection coefficient [4]. If WL statistics is accompanied bymodified deflection measure, WL rule outperforms all otherrules confirming the observations in [9].

Inspired by the recent success of TR-based methods likeTR-MRC and TR-ZF in resolving saturation of SINR owing toresidual ISI and ICI, we have proposed TR-MRC, TR-mMRCand TR-WL rules. However, TR-based rules can suffer fromrestricted performance improvement owing to the limitedinformation available about the environment. In that case,in future, we will resort to space-time spreading of the localSU decisions, before transmission, thereby exploiting multi-slot decisions and even, multi-symbol decisions. If theseextensions are incorporated, such a network will benefitfrom time-integration in sensing performance, opportunisticthroughput and interference-free transmission.

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I. Dey (Member, IEEE) received the M.Sc. degreein wireless communications from the University ofSouthampton, Southampton, U.K., in 2010, and thePh.D. degree in electrical engineering from the Uni-versity of Calgary, Calgary, Canada, in 2015. From2015 to 2016, she was a Post-Doctoral Research Fel-low with the Ultra-Maritime Digital CommunicationCenter, Dalhousie University, Canada. She was aResearch Fellow with the Department of Electronicsand Telecommunications, Norwegian University ofScience and Technology, Trondheim, Norway, from

2016 to 2017. From 2017 to 2019, she was a Marie Skłodowska-Curie(EDGE) Fellow with the Trinity College Dublin, Ireland. She is currently aLecturer/Assistant Professor with the Department of Electronic Engineering,National University of Ireland, Maynooth. She conducts her research at theIrish Research Centre for Future Networks and Communications (CON-NECT). Her current research interests include channel modeling, channelestimation and prediction, adaptive modulation, and dirty tape coding fordifferent wireless propagation environments, and wireless sensor networks.In 2016, she received the prestigious Alain Bensoussan Research Fellowshipfrom the European Research Consortium for Information and Mathematics(ERCIM).

P. Salvo Rossi (Senior Member, IEEE) was born inNaples, Italy, in April 1977. He received the Dr.Eng.degree in telecommunications engineering (summacum laude) and the Ph.D. degree in computer engi-neering from the University of Naples “Federico II”,Italy, in 2002 and 2005, respectively. From 2005 to2008, he has worked as a Post-Doctoral Researcherwith the Department of Computer Science and Sys-tems, University of Naples “Federico II”, the Depart-ment of Information Engineering, Second Universityof Naples, Italy, and the Department of Electron-

ics and Telecommunications, Norwegian University of Science and Tech-nology (NTNU), Norway. From 2008 to 2014, he was an Assistant Professor

(tenured in 2011) in telecommunications with the Department of Industrial andInformation Engineering, Second University of Naples. From 2014 to 2016,he was an Associate Professor in signal processing with the Department ofElectronics and Telecommunications, NTNU. From 2016 to 2017, he was aFull Professor in signal processing with the Department of Electronic Systems,NTNU. From 2017 to 2019, he was a Principal Engineer with the Depart-ment of Advanced Analytics and Machine Learning, Kongsberg Digital AS,Norway. He held visiting appointments at the Department of Electrical andComputer Engineering, Drexel University, USA, the Department of Electricaland Information Technology, Lund University, Sweden, the Department ofElectronics and Telecommunications, NTNU, and the Excellence Center forWireless Sensor Networks, Uppsala University, Sweden. Since 2019, he hasbeen a Full Professor in statistical machine learning with the Department ofElectronic Systems, NTNU, where he is also the Director of IoT@NTNU. Hisresearch interests fall within the areas of communication theory, data fusion,machine learning, and signal processing. He was awarded as an ExemplarySenior Editor for IEEE COMMUNICATIONS LETTERS in 2018. He was anAssociate Editor and a Senior Editor for IEEE COMMUNICATION LETTERS

from 2012 to 2016 and 2016 to 2019, respectively. He has been serving as anExecutive Editor for IEEE COMMUNICATION LETTERS since 2019, an AreaEditor for IEEE OPEN JOURNAL OF THE COMMUNICATIONS SOCIETYsince 2019, an Associate Editor for IEEE TRANSACTIONS ON SIGNAL AND

INFORMATION PROCESSING OVER NETWORKS since 2019, and an AssociateEditor for IEEE TRANSACTIONS ON WIRELESS COMMUNICATION since2015.

M. Majid Butt (Senior Member, IEEE) received theM.Sc. degree in digital communications from Chris-tian Albrechts University, Kiel, Germany, in 2005,and the Ph.D. degree in telecommunications fromthe Norwegian University of Science and Technol-ogy, Trondheim, Norway, in 2011. He is currently aSenior Scientist 5G+ Research at Nokia Bell Labs,France, and a Visiting Research Assistant Professorwith the Trinity College Dublin, Ireland. Before that,he has held various positions at the University ofGlasgow, U.K., the Trinity College Dublin, Ireland,

Fraunhofer HHI, Germany, and the University of Luxembourg. His majorareas of research interest include communication techniques for wirelessnetworks with a focus on radio resource allocation, scheduling algorithms,energy efficiency, and machine learning for RAN. He has authored more than60 peer reviewed conference and journal publications in these areas. He was arecipient of the Marie Curie Alain Bensoussan Postdoctoral Fellowship fromEuropean Research Consortium for Informatics and Mathematics (ERCIM).He has served as the organizer/chair for various technical workshops onvarious aspects of communication systems in conjunction with major IEEEconferences, including WCNC, Globecom, and Greencom. He has beenserving as an Associate Editor for IEEE ACCESS journal and IEEE Com-munication Magazine since 2016.

Nicola Marchetti (Senior Member, IEEE) receivedthe Ph.D. degree in wireless communications fromAalborg University, Denmark, in 2007, the M.Sc.degree in electronic engineering from the Universityof Ferrara, Italy, in 2003, and the M.Sc. degreein mathematics from Aalborg University in 2010.He performs his research under the Irish ResearchCentre for Future Networks and Communications(CONNECT), where he leads the Wireless Engi-neering and Complexity Science (WhyCOM) Lab.He is currently an Associate Professor in wireless

communications at Trinity College Dublin, Ireland. He has authored in excessof 140 journals and conference papers, two books and eight book chapters,holds four patents, and received four best paper awards. His research interestsinclude radio resource management, self-organizing networks, complex sys-tems science, and signal processing for communication networks. He servesas an Associate Editor for the IEEE INTERNET OF THINGS Journal since2018, and the EURASIP Journal on Wireless Communications and Networkingsince 2017.


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